Representing Their Ages Algebraically

Oct 13, 2025 by vinooalluri.com 21 views

Introduction

In this article, we will explore a mathematical problem involving the ages of Karim, his brother Azam, and their father. We will use algebraic expressions to represent their current ages and then calculate their ages after 5 years.

The Problem

Karim is x years old. His brother Azam is 5 years older than him, so Azam's age can be represented as x + 5. Their father is 3 times as old as Azam, so their father's age can be represented as 3(x + 5).

Representing Their Ages Algebraically

Let's represent their current ages using algebraic expressions:

Karim's age: x
Azam's age: x + 5
Father's age: 3(x + 5)

Calculating Their Ages After 5 Years

To calculate their ages after 5 years, we need to add 5 to each of their current ages.

Karim's age after 5 years: x + 5
Azam's age after 5 years: (x + 5) + 5 = x + 10
Father's age after 5 years: 3(x + 5) + 5 = 3x + 15 + 5 = 3x + 20

The Sum of Their Ages After 5 Years

To find the sum of their ages after 5 years, we need to add their individual ages together.

Sum of their ages after 5 years = (x + 5) + (x + 10) + (3x + 20) = 5x + 35

Solving for x

Since we are given that Karim is x years old, we can use this information to solve for x. However, we are not given any specific value for x. Therefore, we will leave the expression in terms of x.

Conclusion

In this article, we used algebraic expressions to represent the ages of Karim, Azam, and their father. We then calculated their ages after 5 years and found the sum of their ages after 5 years. The sum of their ages after 5 years is 5x + 35.

Example Use Case

Suppose we know that Karim is 20 years old. We can substitute this value into the expression for the sum of their ages after 5 years.

Sum of their ages after 5 years = 5x + 35 = 5(20) + 35 = 100 + 35 = 135

Therefore, the sum of their ages after 5 years is 135.

Real-World Applications

This problem can be applied to real-world scenarios where we need to calculate the ages of individuals or groups of people after a certain period of time. For example, in a family planning scenario, we may need to calculate the ages of children and their parents after a certain number of years.

Mathematical Concepts

This problem involves the following mathematical concepts:

Algebraic expressions
Addition
Substitution

Key Takeaways

Algebraic expressions can be used to represent the ages of individuals or groups of people.
Addition can be used to calculate the ages of individuals or groups of people after a certain period of time.
Substitution can be used to solve for unknown values in algebraic expressions.

References

[1] "Algebraic Expressions" by Math Open Reference
[2] "Addition" by Math Is Fun
[3] "Substitution" by Khan Academy
Karim's Family Ages: A Mathematical Puzzle - Q&A =====================================================

Introduction

In our previous article, we explored a mathematical problem involving the ages of Karim, his brother Azam, and their father. We used algebraic expressions to represent their current ages and then calculated their ages after 5 years. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q: What is the current age of Karim's brother Azam?

A: Azam's current age is x + 5, where x is Karim's current age.

Q: How old will Azam be after 5 years?

A: Azam will be x + 10 after 5 years.

Q: What is the current age of Karim's father?

A: Karim's father's current age is 3(x + 5), where x is Karim's current age.

Q: How old will Karim's father be after 5 years?

A: Karim's father will be 3x + 20 after 5 years.

Q: What is the sum of their ages after 5 years?

A: The sum of their ages after 5 years is 5x + 35.

Q: Can we solve for x if we know the sum of their ages after 5 years?

A: Yes, we can solve for x if we know the sum of their ages after 5 years. However, we would need to know the specific value of the sum.

Q: What if we know that Karim is 20 years old? Can we find the sum of their ages after 5 years?

A: Yes, we can find the sum of their ages after 5 years if we know that Karim is 20 years old. The sum of their ages after 5 years would be 5(20) + 35 = 135.

Q: Can we apply this problem to real-world scenarios?

A: Yes, this problem can be applied to real-world scenarios where we need to calculate the ages of individuals or groups of people after a certain period of time.

Q: What are some common mathematical concepts used in this problem?

A: Some common mathematical concepts used in this problem include algebraic expressions, addition, and substitution.